A large number of publications available on determining the feasible region and the operability limits for a design are all limited due to the assumption that the feasible space is convex, but almost all of the problems appearing in chemical engineering are nonconvex in nature. Determining the region where the design is feasible and safe to operate is of extreme importance. To address this problem, a novel algorithm was developed based on the idea of systematically evaluating the infeasibility areas using the outer approximation procedure introduced earlier, and the simplicial approximation approach to approximate the expanded feasible space constructed with the exclusion of the nonconvex constraints. This approach is general and deals with any nonconvex regions, as long as the nonconvex constraints are either concave or quasi-convex, as illustrated through a series of example problems. A new metric is introduced to accommodate the need for comparison between various designs.